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Statistical distributions

Author: Evans, Merran ; Hastings, Nicholas ; Peacock, Brian Series: Wiley series in probability and statistics Publisher: Wiley, 2000.Edition: 3rd ed.Language: EnglishDescription: 221 p. : Graphs ; 23 cm.ISBN: 0471371246Type of document: BookBibliography/Index: Includes bibliographical references
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Item type Current location Collection Call number Status Date due Barcode Item holds
Book Europe Campus
Main Collection
Print QA273 .E83 2000
(Browse shelf)
001253535
Available 001253535
Total holds: 0

Includes bibliographical references

Digitized

Statistical Distributions Contents Preface 1. Introduction 2. Terms and Symbols 2.1 Probability, Random Variable, Variate, and Random Number, 3 2.2 Range, Quantile, Probability Statements and Domain, and Distribution Function, 5 2.3 Inverse Distribution and Survival Function, 8 2.4 Probability Density Function and Probability Function, 9 2.5 Other Associated Functions and Quantities, 11 3. General Variate Relationships 3.1 Introduction, 17 3.2 Function of a Variate, 17 3.3 One-to-One Transformations and Inverses, 18 3.4 Variate Relationships Under One-to-One Transformation, 20 3.5 Parameters, Variate, and Function Notation, 22 3.6 Transformation of Location and Scale, 24 3.7 Transformation from the Rectangular Variate, 25 17 xv 1 3 3.8 Many-to-One Transformations, 26 3.9 Functions of Several Variates, 29 4. Bernoulli Distribution 4.1 Random Number Generation, 32 4.2 Curtailed Bernoulli Trial Sequences, 32 4.3 Urn Sampling Scheme, 33 4.4 Note, 33 5. Beta Distribution 5.1 Notes on Beta and Gamma Functions, 35 5.2 Variate Relationships, 37 5.3 Parameter Estimation, 40 5.4 Random Number Generation, 41 5.5 Inverted Beta Distribution, 41 5.6 Noncentral Beta Distribution, 42 5.7 Beta Binomial Distribution, 42 6. Binomial Distribution 6.1 Variate Relationships, 44 6.2 Parameter Estimation, 46 6.3 Random Number Generation, 47 7. Cauchy Distribution 7.1 Note, 49 7.2 Variate Relationships, 49 7.3 Random Number Generation, 50 7.4 Generalized Form, 50 8. Chi-Squared Distribution 8.1 Variate Relationships, 53 8.2 Random Number Generation, 57 8.3 Chi Distribution, 57 52 48 43 34 31 9. Chi-Squared (Noncentral) Distribution 9.1 Variate Relationships, 59 10. Dirichlet Distribution 10.1 Variate Relationships, 62 10.2 Dirichlet Multinomial Distribution, 63 11. Empirical Distribution Function 11.1 Estimation from Uncensored Data, 65 11.2 Estimation from Censored Data, 66 11.3 Parameter Estimation, 67 11.4 Example, 67 11.5 Graphical Method for the Modified OrderNumbers, 69 11.6 Model Accuracy, 70 12. Erlang Distribution 12.1 Variate Relationships, 72 12.2 Parameter Estimation, 73 12.3 Random Number Generation, 73 13. Error Distribution 13.1 Note, 75 13.2 Variate Relationships, 76 14. Exponential Distribution 14.1 Note, 79 14.2 Variate Relationships, 80 14.3 Parameter Estimation, 81 14.4 Random Number Generation, 81 15. Exponential Family 15.1 Members of the Exponential Family, 82 58 62 65 71 74 77 82 15.2 Univariate One-Parameter Exponential Family, 82 15.3 Estimation, 84 16. Extreme Value (Gumbel) Distribution 16.1 Note, 86 16.2 Variate Relationships, 86 16.3 Parameter Estimation, 89 16.4 Random Number Generation, 89 17. F (Variance Ratio) or Fisher­Snedecor Distribution 17.1 Variate Relationships, 91 18. F (Noncentral) Distribution 18.1 Variate Relationships, 96 19. Gamma Distribution 19.1 Variate Relationships, 99 19.2 Parameter Estimation, 101 19.3 Random Number Generation, 102 19.4 Inverted Gamma Distribution, 103 19.5 Normal Gamma Distribution, 103 19.6 Generalized Gamma Distribution, 104 20. Geometric Distribution 20.1 Notes, 107 20.2 Variate Relationships, 108 20.3 Random Number Generation, 108 21. Hypergeometric Distribution 21.1 Note, 111 21.2 Variate Relationships, 111 21.3 Parameter Estimation, 112 21.4 Random Number Generation, 112 109 106 98 95 90 85 21.5 Negative Hypergeometric Distribution, 21.6 Generalized Hypergeometric (Series) Distribution, 22. Inverse Gaussian (Wald) Distribution 22.1 Variate Relationships, 115 22.2 Parameter Estimation, 116 23. Laplace Distribution 23.1 Variate Relationships, 118 23.2 Parameter Estimation, 120 23.3 Random Number Generation, 120 24. Logarithmic Series Distribution 24.1 Variate Relationships, 122 24.2 Parameter Estimation, 122 25. Logistic Distribution 25.1 Notes, 126 25.2 Variate Relationships, 127 25.3 Parameter Estimation, 128 25.4 Random Number Generation, 128 26. Lognormal Distribution 26.1 Variate Relationships, 130 26.2 Parameter Estimation, 133 26.3 Random Number Generation, 133 27. Multinomial Distribution 27.1 Variate Relationships, 136 27.2 Parameter Estimation, 136 28. Multivariate Normal (Multinormal) Distribution 28.1 Variate Relationships, 138 28.2 Parameter Estimation, 139 112 113 114 117 121 124 129 134 137 29. Negative Binomial Distribution 29.1 Note, 142 29.2 Variate Relationships, 142 29.3 Parameter Estimation, 144 29.4 Random Number Generation, 144 30. Normal (Gaussian) Distribution 30.1 Variate Relationships, 146 30.2 Parameter Estimation, 150 30.3 Random Number Generation, 150 31. Pareto Distribution 31.1 Note, 153 31.2 Variate Relationships, 153 31.3 Parameter Estimation, 154 31.4 Random Number Generation, 154 32. Poisson Distribution 32.1 Note, 157 32.2 Variate Relationships, 157 32.3 Parameter Estimation, 160 32.4 Random Number Generation, 160 33. Power Function Distribution 33.1 Variate Relationships, 162 33.2 Parameter Estimation, 164 33.3 Random Number Generation, 164 34. Power Series (Discrete) Distribution 34.1 Note, 166 34.2 Variate Relationships, 166 33.3 Parameter Estimation, 166 35. Rayleigh Distribution 35.1 Variate Relationships, 168 35.2 Parameter Estimation, 169 140 145 151 155 161 165 167 36. Rectangular (Uniform) Continuous Distribution 36.1 Variate Relationships, 171 36.2 Parameter Estimation, 174 36.3 Random Number Generation, 174 37. Rectangular (Uniform) Discrete Distribution 37.1 General Form, 176 37.2 Parameter Estimation, 177 38. Student's t Distribution 38.1 Variate Relationships, 180 38.2 Random Number Generation, 183 39. Student's t (Noncentral) Distribution 39.1 Variate Relationships, 186 40. Triangular Distribution 40.1 Variate Relationships, 188 40.2 Random Number Generation, 188 41. von Mises Distribution 41.1 Note, 190 41.2 Variate Relationships, 191 41.3 Parameter Estimation, 191 42. Weibull Distribution 42.1 Note, 193 42.2 Variate Relationships, 194 42.3 Parameter Estimation, 194 42.4 Random Number Generation, 196 42.5 Three-Parameter Weibull Distribution, 196 42.6 Three-Parameter Weibull Random Number Generation, 197 42.7 Bi-Weibull Distribution, 197 170 175 178 184 187 189 192 42.8 Five-Parameter Bi-Weibull Distribution, 199 42.9 Weibull Family, 202 43. Wishart (Central) Distribution 43.1 Note, 205 43.2 Variate Relationships, 205 44. Computing References 45. Statistical Tables 45.1 Normal Distribution Function, 211 45.2 Percentiles of the Chi-Squared Distribution, 212 45.3 Percentiles of the F Distribution, 214 45.4 Percentiles of the Student's t Distribution, 218 45.5 Partial Expectations for the Standard Normal Distribution, 219 Bibliography 220 206 210 204

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